Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

Cost-effectiveness of replacing versus discarding the nail in children with nail bed injury

Every year in the UK, around 10 000 children need to have operations to mend injuries to the bed of their fingernails. Currently, most children have their fingernail placed back on the injured nail bed after the operation. The NINJA trial found that children were slightly less likely to have an infection if the nail was thrown away rather than being put back, but the difference between groups was small and could have be due to chance. This study looked at whether replacing the nail is cost-effective compared with throwing it away. Using data from the NINJA trial, we compared costs, healthcare use, and quality of life and assessed the cost-effectiveness of replacing the nail. It was found that throwing the nail away after surgery would save the National Health Service (NHS) £75 (€85) per operation compared with placing the nail back on the nail bed. Changing clinical practice could save the NHS in England £720 000 (€819 000) per year

The polarized image of a synchrotron-emitting ring of gas orbiting a black hole

High Energy Astrophysic

Constraints on black-hole charges with the 2017 EHT observations of M87*

InstrumentationHigh Energy Astrophysic

The variability of the black hole image in M87 at the dynamical timescale

The black hole images obtained with the Event Horizon Telescope (EHT) are expected to be variable at the dynamical timescale near their horizons. For the black hole at the center of the M87 galaxy, this timescale (5–61 days) is comparable to the 6 day extent of the 2017 EHT observations. Closure phases along baseline triangles are robust interferometric observables that are sensitive to the expected structural changes of the images but are free of station-based atmospheric and instrumental errors. We explored the day-to-day variability in closure-phase measurements on all six linearly independent nontrivial baseline triangles that can be formed from the 2017 observations. We showed that three triangles exhibit very low day-to-day variability, with a dispersion of ∼3°–5°. The only triangles that exhibit substantially higher variability (∼90°–180°) are the ones with baselines that cross the visibility amplitude minima on the u–v plane, as expected from theoretical modeling. We used two sets of general relativistic magnetohydrodynamic simulations to explore the dependence of the predicted variability on various black hole and accretion-flow parameters. We found that changing the magnetic field configuration, electron temperature model, or black hole spin has a marginal effect on the model consistency with the observed level of variability. On the other hand, the most discriminating image characteristic of models is the fractional width of the bright ring of emission. Models that best reproduce the observed small level of variability are characterized by thin ring-like images with structures dominated by gravitational lensing effects and thus least affected by turbulence in the accreting plasmas.https://iopscience.iop.org/article/10.3847/1538-4357/ac332e/pdfPublished versio

Resolving the inner parsec of the blazar J1924-2914 with the event horizon telescope

Galaxie

A universal power-law prescription for variability from synthetic images of black hole accretion flows

Instrumentatio

Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

InstrumentationLarge scale structure and cosmolog